Find the Exact Value sin(pi/6)cos(pi/2)+cos(pi/6)sin(pi/2)

$\sin (\frac{π}{6}) \cos (\frac{π}{2}) + \cos (\frac{π}{6}) \sin (\frac{π}{2})$

Step 1

Simplify each term.

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$\frac{1}{2} \cos (\frac{π}{2}) + \cos (\frac{π}{6}) \sin (\frac{π}{2})$

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$\frac{1}{2} \cdot 0 + \cos (\frac{π}{6}) \sin (\frac{π}{2})$

Multiply $\frac{1}{2}$ by $0$ .

$0 + \cos (\frac{π}{6}) \sin (\frac{π}{2})$

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$0 + \frac{\sqrt{3}}{2} \sin (\frac{π}{2})$

The exact value of $\sin (\frac{π}{2})$ is $1$ .

$0 + \frac{\sqrt{3}}{2} \cdot 1$

Multiply $\frac{\sqrt{3}}{2}$ by $1$ .

$0 + \frac{\sqrt{3}}{2}$

Step 2

Add $0$ and $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{2}$

Decimal Form:

$0.86602540 \dots$